Yes, only a very sick person would keep anything in their cup holder other than a cup. Ideally, you should not permit gaudy paper cups with commercial logos to reside in your cup holders, but it's okay to do that in a pinch. Certainly you should pull off the road and dispose of any disposable cup at the first opportunity to do so safely, in an environmentally friendly manner.

Most of the time if I have a cup in my cup holder, it's a Thermos insulated cup. Admittedly, it does have a logo, but since it's an iconic American brand, like Jeep, I am able to rationalize this minor aesthetic affront. However, I am considering debadging it.